## Linear Operators: General theory |

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Page 88

1x = p ( x ) + p ( - x ) , then this

separability

the Hahn - Banach theorem to hold when the field of scalars is non ...

1x = p ( x ) + p ( - x ) , then this

**condition**is sufficient . Bonsall ( 1 ) showed that theseparability

**condition**cannot be dropped . Ingleton [ 1 ] has given**conditions**forthe Hahn - Banach theorem to hold when the field of scalars is non ...

Page 131

To prove the sufficiency of the

satisfies this

and imaginary parts satisfy the same

...

To prove the sufficiency of the

**condition**we observe first that a set function 2satisfies this

**condition**if and only if the positive and negative variations of its realand imaginary parts satisfy the same

**condition**. Thus , it may be assumed that i is...

Page 487

6 , the

subset of C ( $ * ) . It follows from Theorem IV . 6 . 7 , that T ( S ) is conditionally

compact in the metric of Y if and only if the

6 , the

**condition**is equivalent to the statement that T ( S ) is an equicontinuoussubset of C ( $ * ) . It follows from Theorem IV . 6 . 7 , that T ( S ) is conditionally

compact in the metric of Y if and only if the

**condition**is satisfied . Q . E . D . 6 .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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